Cannot Rotate Objects in Object Mode
It's hard to say what you're doing without more info, but if you are only attempting to rotate one object, make sure that you have Manipulate Center Points disabled:



Other than that, in Object Mode, simply press "R", use the mouse to rotate, then Left Click or press Enter to apply the rotation.  This toolbar on the side is for precision, after-the-fact editing.  Changing the angle will rotate the object.